First-order Bessel function

Here Jo and J are the zeroth- and first-order Bessel functions and Ak are the roots of the equation... 

Fig. 7. (a) Wave pattern generated on a circle with scaled radius kr = 1.82. The pattern is the product of a radial part, J,(kr) [the first-order Bessel function] and an angular part, cos ( >- The dashed nodal line of zero (i.e., steady state) concentration runs along diameter of the circle from < > = 90° to < > = 270°. The dotted circle outlines the circular radius. (b) Wave pattern, JAkr) cos 2dashed lines are crossed nodal lines on two perpendicular diameters, (c) Pattern generated at a scaled radius of 3.8, where the zero in the derivative of JAkr) matches the radial boundary condition. The pattern is JAkr) cos 0c >, which has no angular variation. The nodal line is concentric with the outer radius. 

First order Bessel function Absorption coefficient Boltzmann constant Wavelength of laser beam Left circularly polarized light Miscible... 

In these equations 5 is the reciprocal of the X-radiation wave length and bo is the magnitude of the fibrillar axial period (ca. 640 A.). The voa and (Toa are mean values for the respective displacement parameters averaged over the fibrillar levels at which distortion occurs. The symbol Ji signifies the first-order Bessel function whose argument is included after it in parentheses. 

Here, aj is the first root of the first-order Bessel function of the first kind, and a is the surface tension. Note that in the above equation the rate of thinning is inversely proportional to This is in good agreement with some experimental observations. 

Jo and J, are zero-order and first-order Bessel functions. 

J - first-order Bessel functions of the first kind... 

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